give a variable to an operator
I'm presuming that reload_xref is meant to be reload_lib.

In your Reloadlib class you can create a StringProperty to pass the name of the library into:

class Reloadlib(bpy.types.Operator):
    """Reloads the current Library"""
    bl_idname = "my.reload_lib"
    bl_label = "Reload"

    #2.8
    library_name : bpy.props.StringProperty()
    #2.79
    #library_name = bpy.props.StringProperty()


Then in execute you can access this local property with self.library_name:

    def execute(self, context):
        libs[self.library_name].reload()
        self.report({'INFO'}, 'Reloading ' + libs[self.library_name].name)
        return {'FINISHED'}


Then, when you display the operator you can pass in the name:

for i in libs:
    layout.label(text= i.name.replace(".blend",""))
    row = layout.row()
    sub = row.row()
    operator = sub.operator("my.reload_xref", icon = "FILE_REFRESH")
    operator.library_name = i.name


(To be clear, I haven't tested the specific functionality of reloading libraries, but  this is how you pass data generally.)

Full code: 

import bpy

libs = bpy.data.libraries

class Reloadlib(bpy.types.Operator):
    """Reloads the current Library"""
    bl_idname = "my.reload_lib"
    bl_label = "Reload"

    #2.8
    library_name : bpy.props.StringProperty()
    #2.79
    #library_name = bpy.props.StringProperty()

    def execute(self, context):
        libs[self.library_name].reload()
        self.report({'INFO'}, 'Reloading ' + libs[self.library_name].name)
        return {'FINISHED'}

class LibPanel(bpy.types.Panel):
    """Creates a Panel in the scene context of the properties editor"""
    bl_label = "Scene Libraries"
    bl_idname = "SCENE_PT_layout"
    bl_space_type = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context = "scene"

    def draw(self, context):
        layout = self.layout
        scene = context.scene
        layout.label(text="Libraries:")

        for i in libs:
            layout.label(text= i.name.replace(".blend",""))
            row = layout.row()
            sub = row.row()
            operator = sub.operator("my.reload_lib", icon = "FILE_REFRESH")
            operator.library_name = i.name

def register():
    bpy.utils.register_class(Reloadlib)
    bpy.utils.register_class(LibPanel)

def unregister():
    bpy.utils.unregister_class(Reloadlib)
    bpy.utils.unregister_class(LibPanel)

if __name__ == "__main__":
    register()